The proposed merger is still subject to the approval of the board of governors of the Federal Reserve, as well as the Federal Deposit Insurance Corporation.
Officials said they were pleased that the agreement greased the skids for SunTrust and BB&T to consolidate by the end of this year.
"This announcement marks another significant and required step toward the merger of equals between BB&T and SunTrust," Kelly King, chairman and chief executive of Winston-Salem-based BB&T, in said a written statement.
The combined banks will be based in Charlotte and will be named Truist Financial Corp.
For the time being, branches that are not being divested will keep their current branding – either BB&T or SunTrust. The name on consumers' checks, credit cards and debit cards also will not change right away.
First Horizon officials said they see the acquisition as a quick way to pump up the bank’s presence in some key markets.
“First Horizon is excited to welcome new employees and customers to our family,” said Bryan Jordan, First Horizon’s chairman and CEO.